The production of magnetic forces in a magnetic actuator is the focus of the present analysis. Magnetic circuit analysis is used to investigate the direction as well as the expected order of magnitude of the force that attracts the armature into the central portion of a stationary core. A sequence of finite-element based solutions is used to investigate magnetic saturation and to determine the force-displacement characteristic. The analytical approach is based on the principle of virtual work and Ampère's law. The force calculations based on numerical field solutions employ the methods of weighted Maxwell stress tensor and the classical virtual work. The more accurate field-derived solutions are used to explain the limitations of the analytical calculations. At the end, an alternative approach to compute the force numerically is proposed. This method is based on the principle of virtual work, but only one field solution is required.